A nonlinear stability problem in the three dimensional restricted three body problem
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The question of whether or not there is a transfer of energy between the in-plane motion and out-of-plane motion in the neighborhood of L4 in the restricted problem of three bodies is investigated in this paper. The in-plane motion is assumed to be finite and the out-of-plane motion to be infinitesimal. The equation governing the out-of-plane motion becomes one with time varying coefficients. The stability of this equation is then investigated using Lie Series. © 1972 D. Reidel Publishing Company.
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